{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mOtlkKOJk11B"
   },
   "source": [
    "##### Copyright 2019 The TensorFlow Authors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "2CTPLx3Ukwrv"
   },
   "outputs": [],
   "source": [
    "#@title Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "# https://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wSIW5dYmdGfE"
   },
   "source": [
    "# Transformer Position Encoding\n",
    "\n",
    "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/examples/blob/master/community/en/position_encoding.ipynb\">\n",
    "    <img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />\n",
    "    Run in Google Colab</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://github.com/tensorflow/examples/blob/master/community/en/position_encoding.ipynb\">\n",
    "    <img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />\n",
    "    View source on GitHub</a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZPoPd7GbdK0G"
   },
   "source": [
    "See [this notebook](https://github.com/site/en/r2/tutorials/sequences/transformer.ipynb) for a walk-through of full transformer implementation.\n",
    "\n",
    "The transformer architecture uses stacked attention layers in place of CNNs or RNNs. This makes it easy to learn long-range dependencise but it contains no built in information about the relative positions of items in a sequence. \n",
    "\n",
    "To give the model access to this information the transformer architecture uses adda a position encoding to the input.\n",
    "\n",
    "This endocing is a vector of sines and cosines at each position, where each sine-cosine pair rotates at a different frequency.  \n",
    "\n",
    "Nearby locations will have similar position-encoding vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XLC5-V6sefM6"
   },
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "y6BDOVCnKPSW"
   },
   "outputs": [],
   "source": [
    "from __future__ import absolute_import, division, print_function, unicode_literals\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "oCajWknYcYpV"
   },
   "source": [
    "The angle rates range from `1 [rads/step]` to `min_rate [rads/step]` over the vector depth.\n",
    "\n",
    "Formula for angle rate:\n",
    "\n",
    "$$angle\\_rate_d = (min\\_rate)^{d / d_{max}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ADsz4y85ANsB"
   },
   "outputs": [],
   "source": [
    "num_positions = 50\n",
    "depth = 512\n",
    "min_rate = 1/10000\n",
    "\n",
    "assert depth%2 == 0, \"Depth must be even.\"\n",
    "angle_rate_exponents = np.linspace(0,1,depth//2)\n",
    "angle_rates = min_rate**(angle_rate_exponents)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "E51Ne4cNe1i8"
   },
   "source": [
    "The resulting exponent goes from `0` to `1`, causing the `angle_rates` to drop exponentially from `1` to `min_rate`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(256,)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "angle_rate_exponents.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ohldgW_Xg2sC"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Angle rate [rads/step]')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(angle_rates)\n",
    "plt.xlabel('Depth')\n",
    "plt.ylabel('Angle rate [rads/step]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fMaA6pUqh-tQ"
   },
   "source": [
    "Broadcasting a multiply over angle rates and positions gives a map of the position encoding angles as a function of depth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Rs2ABZ3XhYFg"
   },
   "outputs": [],
   "source": [
    "positions = np.arange(num_positions) \n",
    "angle_rads = (positions[:, np.newaxis])*angle_rates[np.newaxis, :] # 50 x 1 : 1 x 256\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 256)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "angle_rads.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "eHEHWQa8_51Z"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (14,8))\n",
    "plt.pcolormesh(\n",
    "    # Convert to degrees, and wrap around at 360\n",
    "    angle_rads*180/(2*np.pi) % 360,\n",
    "    # Use a cyclical colormap so that color(0) == color(360)\n",
    "    cmap='hsv', vmin=0, vmax=360)\n",
    "\n",
    "plt.xlim([0,len(angle_rates)])\n",
    "plt.ylabel('Position')\n",
    "plt.xlabel('Depth')\n",
    "bar = plt.colorbar(label='Angle [deg]')\n",
    "bar.set_ticks(np.linspace(0,360,6+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "MEGyhu_JiNDS"
   },
   "source": [
    "Raw angles are not a good model input (they're either unbounded, or discontinuous). So take the sine and cosine:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "BBnQuSSPGl8t"
   },
   "outputs": [],
   "source": [
    "sines = np.sin(angle_rads)\n",
    "cosines = np.cos(angle_rads)\n",
    "pos_encoding = np.concatenate([sines, cosines], axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 512)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_encoding.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UQrE2_nPHjXC"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f2ad007a898>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14,8))\n",
    "plt.pcolormesh(pos_encoding, \n",
    "               # Use a diverging colormap so it's clear where zero is.\n",
    "               cmap='RdBu', vmin=-1, vmax=1)\n",
    "plt.xlim([0,depth])\n",
    "plt.ylabel('Position')\n",
    "plt.xlabel('Depth')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "e536lUb-k-UQ"
   },
   "source": [
    "## Nearby positions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UzWWHKK1lu0z"
   },
   "source": [
    "Nearby locations will have similar position-encoding vectors. \n",
    "\n",
    "To demonstrate compare one position's encoding (here position 20) with each of the others:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "kruiT670zjrZ"
   },
   "outputs": [],
   "source": [
    "pos_encoding_at_20 = pos_encoding[20]\n",
    "\n",
    "dots = np.dot(pos_encoding,pos_encoding_at_20)\n",
    "SSE = np.sum((pos_encoding - pos_encoding_at_20)**2, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((50, 512), (512,))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_encoding.shape, pos_encoding_at_20.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xH-sU6mzmjXI"
   },
   "source": [
    "Regardless of how you compare the vecors, they are most similar 20, and clearly diverge as you move away: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "YQ-MqQ5Eo0ZT"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Position')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8))\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(dots)\n",
    "plt.ylabel('Dot product')\n",
    "plt.subplot(2,1,2)\n",
    "plt.plot(SSE)\n",
    "plt.ylabel('SSE')\n",
    "plt.xlabel('Position')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BVgAzBJ7iYda"
   },
   "source": [
    "## Relative positions\n",
    "\n",
    "The [paper](https://arxiv.org/pdf/1706.03762.pdf) explains, at the end of section 3.5, that any relative position encoding can be written as a linear function of the current position.\n",
    "\n",
    "To demonstrate, this section builds a matrix that calculates these relative position encodings. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "aHOBuNYnLHFF"
   },
   "outputs": [],
   "source": [
    "def transition_matrix(position_delta, angle_rates = angle_rates):\n",
    "  # Implement as a matrix multiply:\n",
    "  #    sin(a+b) = sin(a)*cos(b)+cos(a)*sin(b)\n",
    "  #    cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b)\n",
    "  \n",
    "  # b\n",
    "  angle_delta = position_delta*angle_rates\n",
    "\n",
    "  # sin(b), cos(b)\n",
    "  sin_delta = np.sin(angle_delta)\n",
    "  cos_delta = np.cos(angle_delta)\n",
    "\n",
    "  I = np.eye(len(angle_rates))\n",
    "  \n",
    "  # sin(a+b) = sin(a)*cos(b)+cos(a)*sin(b)\n",
    "  update_sin = np.concatenate([I*cos_delta, I*sin_delta], axis=0)\n",
    "  \n",
    "  # cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b)\n",
    "  update_cos = np.concatenate([-I*sin_delta, I*cos_delta], axis=0)\n",
    "\n",
    "  return np.concatenate([update_sin, update_cos], axis=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GZKHXFAxkMb_"
   },
   "source": [
    "For example, create the matrix that calculates the position encoding 10 steps back, from the current position encoding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "x31yfQRQM6Q6"
   },
   "outputs": [],
   "source": [
    "position_delta = -10\n",
    "update = transition_matrix(position_delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NznTFtWmklob"
   },
   "source": [
    "Applying this matrix to each position encoding vector gives position encoding vector from -10 steps away, resulting in a shifted position-encoding map:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "hE7t9frqNQV3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Depth')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14,8))\n",
    "plt.pcolormesh(np.dot(pos_encoding,update), cmap='RdBu', vmin=-1, vmax=1)\n",
    "plt.xlim([0,depth])\n",
    "plt.ylabel('Position')\n",
    "plt.xlabel('Depth')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "a1IHJT2Jk16a"
   },
   "source": [
    "This is accurate to numerical precision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "tRmt2d-HQD8j"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.4262150328554526e-15"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errors = np.dot(pos_encoding,update)[10:] - pos_encoding[:-10]\n",
    "abs(errors).max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "collapsed_sections": [],
   "name": "position_encoding.ipynb",
   "private_outputs": true,
   "provenance": [],
   "toc_visible": true,
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  },
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